Dynamically Equivalent Simulator for Vehicle Rotational Motions

ABSTRACT

A vehicle nonlinear dynamics simulation device, such as flight simulator, including a motorized spherical vehicle suspended inside another spherical shell which has smooth inner surface. The spherical vehicle is supported by a plurality of spiky legs of either air-bearing assemblies or omni-directional ball bearing assemblies. The outer spherical shell is supported by three controllable translational motion platforms. Simulating equipment for a pilot cabin is mounted inside the spherical vehicle. The spherical vehicle has driving, restoring, and damping capabilities in roll, pitch, and yaw directions and is capable to rotate 360° in any directions. Therefore it provides a dynamically equivalent model to simulate a vehicle rotational dynamics. The driving and restoring means include Omni wheel assemblies mounted outside of the spherical vehicle and operable to contact the inner surface of the shell to drive the spherical vehicle in roll, pitch, and yaw directions. The driving means include electrical motors. The restoring and damping mechanisms are provided by rotational springs and rotational dampers, respectively. The rotational movements of the spherical vehicle are active and controlled by the driving system and also by the nonlinear dynamics of the spherical vehicle itself, in contrast to the passive movements of the simulation platforms currently used in industries.

FIELD OF THE INVENTION

This invention relates to motion simulator, more specifically a suspended spherical vehicle containing one or more occupants. Possible applications includes nonlinear motion simulations for vehicles like aircrafts, automobiles, and ships; testing bed for design and analyses; pilot training; virtual realities; and 3D game playing.

BACKGROUND OF THE INVENTION

Within the aviation and automobile industries, the most extensively used movable training and testing device is known as Stewart Platform, or hexapod platform. Although a flight simulator using hexapod platform is called a full flight simulator since it provides a six-degree-of-freedom, it is actually not a really full six degrees of freedom. The roll, pitch, and yaw are limited in small ranges. For example, the limitations of roll, pitch, and yaw of the KLM 747 motion base given in the Table 1 of “The generation of motion cues on a six-degree-of-freedom motion system” by M. Baarspul, Report LR-248, Delft University of Technology, 1977, were 28°, 34°, and 36° respectively, not even mention 50°. In reality, however, aircrafts could experience much more rotational motions than those limitations. For example, in 1993 Japan Airlines Flight 46E Boeing 747-121 encountered an uncommanded roll of about 50° (see NTSB/AAR-93/06, PB93-910407). A 360° roll was also experienced by TWA Flight 841 in 1979 (see NTSB-AAR-81-8, PB81-910408). Despite the 100 years aviation history, evidence indicates that when faced with uncommanded roll, pitch, and yaw, pilots sometimes have difficulties in quickly responding to the situation which needs rapid action to correct in order to avoid crash. The trainings of uncommanded roll, pitch, and yaw are either not effective enough or not correct at all. The reason for such awkward situation in the industry is that the mechanism of the uncommanded roll, pitch, and yaw has not been understood. The relationship between fidelities of the current flight simulators and real aircrafts is susceptible when the roll, pitch, and yaw motions become large enough since the current flight dynamics are based on the linearization approximation of roll, pitch, and yaw motions, meaning that the aircraft motions have to be small enough to be accurate.

Even with a simulator capable to rotate to 360° in any axis, like the capsules proposed in U.S. Pat. Nos. 5,060,932, 5,490,784, and 6,629,896, the accuracies of the large motions of these capsules are still questionable because first the motions of these capsules are controlled by computer programs which most likely are based on the linearized dynamics and second no real data (like uncommanded roll, pitch, and yaw) available to calibrate the simulated large motions.

As pointed out in the inventor's book, “Nonlinear Instability and Inertial Coupling Effects—The Root Causes Leading to Aircraft crashes, Land Vehicle Rollovers, and Ship Capsizes” (ISBN978-1-7326323-0-1, to be published in November 2018), these uncommanded roll, pitch, and yaw motions experienced by aircrafts are nonlinear phenomena. Without the infinite rotational freedom of three dimensions and the nonlinear flight dynamics, large rotational motions cannot be simulated accurately. The new scientific discovery given in the inventor's book about the nonlinear instability of vehicle dynamics is summarized below. Vehicles like cars, ships, and aircrafts all have rolling problems. Cars have rollover; ships have rolling and capsizing; and aircrafts have Dutch roll and mysterious crashes. Is it just a coincident that all these three major types of vehicles have the same rolling problem? Or it is not. The fact is that all these vehicles follow a same scientific law and show the same symptom. These vehicles have existed for more than a century. It is believed that the rolling problems have, so far, accounted for accidents and deaths in the level of millions and the cost of injuries in medical care, disability and property damage in trillions of dollars worldwide. This invention is one of several inventions the inventor has invented to deal with those dangerous rolling phenomena in order to save lives on the roads and oceans, and in the sky around the world by applying the new scientific discovery.

From the viewpoint of physics, these vehicles are nothing but rigid body systems of six degrees of freedom (three translational motions in three perpendicular axes, i.e. forward/backward, left/right, up/down; and three rotational motions about three orthogonal axes, often termed roll, pitch, and yaw). Believe it or not, the three rotational (roll, pitch, and yaw) motions under external moments have never been solved analytically without linearization approximation and as a result they have never been understood satisfactorily due to the fact that the governing equations for these motions are nonlinear which was extremely difficult to deal with analytically. Although numerical simulations for those motions have been obtained, the results were often difficult to be explained because of the lack of the correct understanding of the mechanism. Consequently, there have been so many SUV rollovers, airplane crashes, and ship capsizes, which were hard to be explained and have remained mysteries. For example, why some vehicles had many times more rollover fatality rate than other vehicles with the same rollover rating, i.e. Static Stability Factor (SSF). The mysterious airplane crashes include United Airlines Flight 585 in 1991, SilkAir Flight 185 in 1997, EgyptAir Flight 990 in 1999, and American Airlines Flight 587 in 2001 to name a few. Ship broaching and capsizing in severe following seas has not been explained satisfactorily as well.

A fundamental mistake has been made in dealing with the vehicle dynamics in the current academic and industry practices. For a vehicle, no matter it is a car, or an aircraft, the governing equations for its rotational motions (roll, pitch, and yaw) are given by Math.1 in the vector form. They were obtained based on Newton's second law of motions in the body-fixed reference frame,

d{right arrow over (H)}/dt=−{right arrow over (ω)}×{right arrow over (H)}+{right arrow over (M)},  Math. 1

wherein {right arrow over (ω)}=(p,q,r)=({dot over (φ)},{dot over (θ)},{dot over (ψ)}): the angular velocities of the vehicle; φ,θ,ψ: the roll, pitch, and yaw angle about the principal axes of inertias X, Y, Z, respectively; {right arrow over (H)}=(I_(x)p,I_(y)q,I_(z)r): the angular momentum of the vehicle; I_(x),I_(y),I_(z): the moment of inertias about the principal axes of inertias X, Y, Z, respectively (These parameters are constants in this frame); {right arrow over (M)}=(M_(x),M_(y),M_(z)): the external moments acting on the vehicles about the principal axes of inertia. In both the academies and industries related to automobiles, aircrafts, and ships, the current practice to deal with Math. 1 is to make a linearization approximation first and then solve the equations because the nonlinear term −{right arrow over (ω)}×{right arrow over (H)} is too difficult to deal with. The linearization approximation makes the nonlinear term −{right arrow over (ω)}×{right arrow over (H)} disappear, the equations then become

d{right arrow over (H)}/dt={right arrow over (M)}.  Math. 2

However, the equations are still considered in the body-fixed reference frame which is a non-inertial frame. The reason for this is that the external moments (M_(x),M_(y),M_(z)) acting on vehicles and the moments of inertia I_(x),I_(y),I_(z) are needed to be considered in the body-fixed reference frame.

The fundamental mistake is that the nonlinear term −{right arrow over (ω)}×{right arrow over (H)} cannot be neglected because they are the inertial moments tied to the non-inertial reference frame which is the body-fixed reference frame in this case. This mistake is similarly like we neglect the Coriolis force which equals −2{right arrow over (Ω)}×{right arrow over (V)}, where {right arrow over (Ω)} is the angular velocity vector of the earth and {right arrow over (V)} is the velocity vector of a moving body on earth. Then we try to explain the swirling water draining phenomenon in a bathtub. In this case, we are considering the water moving in the body-fixed and non-inertial reference frame which is the earth. The Coriolis force is an inertial force generated by the rotating earth on the moving objects which are the water particles in this case. Without the Coriolis force, we cannot explain the motions of the swirling water. Similarly in the vehicle dynamics, the vehicle is rotating, and we consider the rotational motions of the vehicle in the body-fixed and non-inertial reference frame which is the vehicle itself. The difference between the two cases is that in the former the object (water particle) has translational motions ({right arrow over (V)}) while in the latter the object (vehicle itself) has rotational motions ({right arrow over (ω)}) but they both have the important inertial effects which cannot be neglected because both the objects are considered in the non-inertial reference frames. In the former the inertial effect is the Coriolis force −2{right arrow over (Ω)}×{right arrow over (V)} while in the latter the inertial effect is the inertial moment −{right arrow over (ω)}×{right arrow over (H)} which are not forces but moments since we are dealing with rational motions instead of translational one. Without the inertial moment, we cannot explain many phenomena which happened to aircrafts, automobiles, and ships, such as uncommanded motions of roll, pitch, and yaw for aircrafts; Pilot-Induced-Oscillation (PIO) for aircrafts; automobile rollovers; and ship capsizes.

In the inventor's book, the equations Math.1 have been solved analytically without the linearization approximation and it was found that the pitch motion, without loss of generality assuming the pitch moment of inertia to be the intermediate between the roll and yaw inertias, is conditionally stable and becomes unstable in certain circumstances. A brief summary of the findings is given below. The governing equations of rotational motions of an aircraft or an automobile under a periodic external pitch moment can be written in scalar form as

I _(x) {umlaut over (φ)}+b ₁ {dot over (φ)}+k ₁φ=(I _(y) −I _(z)){dot over (θ)}{dot over (ψ)},  Math. 3

I _(y) {umlaut over (θ)}+b ₂ {dot over (θ)}+k ₂θ=(I _(z) −I _(x)){dot over (φ)}{dot over (ψ)}+M ₂₁ cos(ω₂₁ t+α ₂₁),  Math. 4

I _(z) {umlaut over (ψ)}+b ₃ {dot over (ψ)}+k ₃ψ=(I _(x) −I _(y)){dot over (φ)}{dot over (θ)},  Math. 5

wherein b₁,b₂,b₃ are the damping coefficients for roll, pitch, and yaw, respectively; k₁,k₂,k₃ are the restoring coefficients for roll, pitch, and yaw, respectively; M₂₁ is the external pitch moment amplitude; ω₂₁ and α₂₁ are the frequency and phase of the external pitch moment, respectively. These equations represent a dynamic system governing the rotational dynamics of vehicles, such as an aircraft when taking off or approaching to landing or an automobile when running off the curb where the most fatal rollovers happen. According to the current practice in the industries under the linearization approximation, these equations become

I _(x) {umlaut over (φ)}+b ₁ {dot over (φ)}+k ₁φ=0,  Math. 6

I _(y) {umlaut over (θ)}+b ₂ {dot over (θ)}+k ₂ θ=M ₂₁ cos(ω₂₁ t+α ₂₁),  Math. 7

I _(z) {umlaut over (ψ)}+b ₃ {dot over (ψ)}+k ₃ψ=0.  Math. 8

Therefore the current practice says that the vehicle will only have pitch motion, no roll and yaw motions because there are no moments acting on roll and yaw directions. In reality, however, there exist moments acting in roll and yaw directions as indicated by the nonlinear terms in the right hand sides of Math. 3 and Math. 5, respectively. These moments are the components of the inertial moment vector −{right arrow over (ω)}×{right arrow over (H)} along roll and yaw directions, respectively, and they are real and must not be neglected. The linearization theory assumes that these nonlinear terms are small so that they can be neglected. The fact is that this assumption is not always valid. The reason is explained below. The roll and yaw dynamic systems of vehicles are harmonic oscillation systems as shown in Math. 3 and Math. 5. As we know for a harmonic system, a resonance phenomenon can be excited by a driving mechanism no matter how small it is as long as its frequency matches the natural frequency of the system. It was found in the inventor's book mentioned above that under certain circumstances the nonlinear terms, (I_(y)−I_(z)){dot over (θ)}{dot over (ψ)} and (I_(x)−I_(y)){dot over (φ)}{dot over (θ)} can simultaneously excite roll and yaw resonances, respectively. In these cases, the pitch motion becomes unstable and the roll and yaw motions grow exponentially at the same time under the following two conditions, Math. 9 and Math. 10. Such nonlinear instability is a phenomenon of double resonances, i.e. roll resonance in addition to yaw resonance.

$\begin{matrix} {{{A_{P} > A_{P - {TH}}} = {{\frac{1}{\omega_{21}}\sqrt{\frac{b_{1}b_{3}}{\left( {I_{z} - I_{y}} \right)\left( {I_{y} - I_{x}} \right)}}\mspace{14mu} {and}\mspace{14mu} \omega_{21}} = {\omega_{10} + \omega_{30}}}},} & {{Math}.\mspace{14mu} 9} \\ {{{A_{P} > A_{P - {TH}}} = {{\frac{1}{\omega_{21}}\sqrt{\frac{b_{1}b_{3}}{\left( {I_{z} - I_{y}} \right)\left( {I_{y} - I_{x}} \right)}}\mspace{14mu} {and}\mspace{14mu} \omega_{21}} = {{\omega_{10} + \omega_{30}}}}},} & {{Math}.\mspace{14mu} 10} \end{matrix}$

wherein A_(P) is the pitch response amplitude under the external pitch moment M₂₁ cos(ω₂₁t+α₂₁); ω₁₀=√{square root over (k₁/I_(x))} and ω₃₀=√{square root over (k₃/I_(z))} are the roll and yaw natural frequencies, respectively. The nonlinear dynamics says that the pitch motion is stable until the pitch motion reaches the threshold values A_(P-TH) given in Math. 9 or Math.10. These threshold values show that the vehicle has two dangerous exciting frequencies in pitch. These two frequencies are either the addition of the roll natural frequency ω₁₀ and the yaw natural frequency ω₃₀ or the subtraction of them. At each frequency, the pitch amplitude threshold for pitch to become unstable is inversely proportional to the pitch exciting frequency, proportional to the square root of the product of the roll and yaw damping coefficients, and inversely proportional to the square root of the product of the difference between the yaw and pitch moments of inertia and the difference between the pitch and roll moments of inertia. In summary, there are three factors having effects on the pitch threshold and they are a) the roll and yaw damping, b) the pitch exciting frequency, and c) the distribution of moments of inertia. The most dominant one among these three factors is the damping effect since the damping coefficients could go to zero in certain circumstances, for example, aircraft yaw damper malfunction which makes the yaw damping become zero, or aircraft in stall condition which makes the roll damping become zero. When either the roll damping or the yaw damping is approaching to zero, the pitch threshold is approaching to zero as well and the pitch motion, even it is small but as long as larger than the threshold value, will become unstable and transfer energy to excite roll and yaw resonances. That is the root mechanism behind all these mysterious tragedies mentioned above. In the inventor's book detailed scientific proofs based on analytical, numerical, and experimental results have been given. Many real case analyses, like aircraft crashes and SUV rollovers, have been given as well. The inventor's another U.S. patent application Ser. No. 16/153,883 is related to an apparatus used as a demonstrator in the book to demonstrate the phenomenon of nonlinear pitch instability.

Therefore there is a need for a motion simulator which can provide a test bed, first to be capable to show the nonlinear instability, second to be used for training pilots or vehicle operators on how to avoid this nonlinear instability and how to recover from this instability if they got into that situation in the first place, third to provide nonlinear (larger) motion data for calibrating a passive-motion simulators, and last to test and analyze the nonlinear dynamics of new designs of vehicles, such as aircrafts, automobiles, and ships.

SUMMARY OF THE INVENTION

The principal objective of the present invention is to provide a mechanical simulator to be used to perform nonlinear vehicle dynamics and to be used for training, simulation purposes, control analyses, and designs of vehicles which include, but not limited to, aircrafts, automobiles, and ships. The present invention allows a user to create a mechanical simulator having rigid body rotational dynamics equivalent with that of a full scale vehicle to be simulated and provide a test bed to perform fully nonlinear rotational dynamic simulations for vehicles, such as aircrafts, automobiles, and ships etc. The most critical applications of this invention include simulations of unconventional phenomena and evaluations of unconventional designs for which no experience base exists for such conditions including flight at high angles of attack, stall, and spins for aircrafts. In these conditions large dynamic motions are typically encountered.

In one embodiment, the present invention includes a motorized spherical vehicle suspended inside another spherical shell by a plurality of air bearing supports so that the spherical vehicle has infinite degrees of rotational freedom in roll, pitch, and yaw directions. The air bearing supports are mounted outside of the spherical vehicle in a distribution pattern and diametrically opposed in pairs such that the spherical vehicle weight is always supported by a plurality of air bearings at all times during rotational motions. The spherical shell has smooth inner surface to allow the air bearings to work efficiently to support the spherical vehicle to rotate easily and smoothly. Six drive assemblies on the spherical vehicle are responsible to drive the spherical vehicle in rotational movements in roll, pitch, and yaw directions. Six restoring and damping assemblies on the spherical vehicle are responsible to apply restoring moments and damping moments in roll, pitch, and yaw directions. The moments of inertias, the restoring coefficients and the damping coefficients in roll, pitch, and yaw directions of the spherical vehicle are to be tuned and designed to be scaled down at a predetermined ratio comparing with that of the real vehicle to be simulated, and similarly the applied moments along roll, pitch, and yaw directions are also scaled down at the same ratio. The outer spherical shell is supported by three controllable translational motion platforms. Simulating equipments for a pilot cabin are mounted inside the spherical vehicle. In this invention, the translational movements (surge, sway, and heave) of the spherical vehicle are passive and controlled by a simulating computer. However, the rotational movements (roll, pitch, and yaw) of the spherical vehicle as one rigid body are ACTIVE and controlled by the control inputs and also by the nonlinear dynamics of the rigid body itself, in contrast to the PASSIVE movements of the simulation platforms controlled totally by computers commonly used in the current industry practices.

The outer spherical shell includes one bottom dome structure and one top dome structure with the same size. Each of the dome structures includes at least two layers. The outer layer includes a plurality of identical frame panels. Preferably, these panels are to be made of fiber-reinforced composite materials to provide enough strength to support the weight of the spherical vehicle. The outer layer panel has smooth inner surface and outside skeletal frames. These panels are fastened together by bolts through the frames to form a half sphere dome. The inner layer includes a thin, hard, and air-tight half sphere dome layer with extremely smooth inner surface. Preferably, the inner layer is seamless except at the door frame in the top dome and at the location where the top and bottom domes meet. The inner layer is bonded with the outer layer to form a solid half sphere dome. The top half sphere dome is fastened with the bottom half sphere dome by bolts through the frames in the great circles of the two domes to form a solid spherical shell. On the top half sphere dome, there is a purposely build door capable to be open and closed tight from the outside to allow people to get in and out of the spherical vehicle. The door frame is a cut-out from one of the bottom panel of the top sphere dome. The door is made similarly and with the same material as the spherical shell with additional reinforced frames bonded on the outside surface of the door and has a same smooth, air-tight and spherical shape inner surface. When the door is closed a perfect air-tight spherical shell is formed. The translational motions (surge, sway, and heave) of the spherical shell may be remotely controlled by computers on-board the spherical vehicle or controlled by computers located outside of the spherical shell with communication means to the spherical vehicle.

The spherical vehicle includes a spherical skeleton made of ring beams, a plurality of the air bearing support assemblies, a plurality of the drive assemblies, a plurality of the restoring and damping assemblies, a platform, a pilot cabin, and control equipments such as batteries, air compressors, computers, screens, etc. Preferably, these ring beams are made of fiber-reinforced composite materials or light metal such as aluminum to provide strong bending strength and light weight. The radiuses of all the ring beams are same and designed based on a cube as shown in FIG. 13a . There are nine ring beams in the example. Three ring beams are located on the XOY, YOZ, and XOZ planes, respectively. The orientations of the other six ring beams may be found by rotating the above three ring beams ±45° about X, Y, and Z axes, respectively. The nine ring beams are connected with each other to form a solid spherical skeleton as a truss base for the spherical vehicle as shown in FIG. 13b . The nine ring beams contact all the 14 vertices of a tetrakis hexahedron (not shown) formed based on the inside cube shown in FIG. 13a . The tetrakis hexahedron may be imagined as the inside cube with pyramids on each face. The apex of each pyramid coincides with the centers of the four-ring-beam joints (shown in FIG. 13d ) which are also located on X, Y, and Z axes as shown in FIG. 13 a.

Each of the air bearing assemblies includes a support post, a ball connector and a spherical convex air bearing. The air bearing assemblies are radially outward mounted on the ring beams which construct the skeleton for the spherical vehicle. Preferably, the air bearing are located at the locations of the 14 vertices of the tetrakis hexahedron mentioned above. The air bearing is made of porous materials and has a convex spherical curvature substantially matching that of the inner surface of the spherical shell. High pressure air from the on-board air compressors is supplied to the air bearings to form a thin layer of air to allow frictionless motions for the spherical vehicle.

The driving assemblies include six omni wheel units driven by reversible DC motors with variable speed. Preferably each driving omni wheel unit includes one pair of identical driving omni wheels. Each two of those identical driving omni wheel units are mounted outside of the spherical vehicle along a great circle in a diametrically opposed fashion. The six driving omni wheel units are mounted on three great circles which are orthogonal to each other and the normal directions of the three great circles coincide with the directions of roll, pitch, and yaw, respectively. Each driving omni wheel unit is controlled by a linear actuator to be operable to contact and detach the inner surface of the outer spherical shell in order to apply a desired moment on the spherical vehicle in a fixed direction relative to the spherical vehicle body-fixed reference frame. The omni wheels are specially designed to have continuous alternate rollers (e.g. German patent DE822660) to allow smooth movements for the spherical vehicle.

The restoring and damping assemblies include six omni wheel units driven by rotational springs and rotational dampers. Preferably each restoring omni wheel unit includes one pair of identical restoring omni wheels. Similarly, each two of those identical restoring omni wheel units are mounted outside of the spherical vehicle along a great circle in a diametrically opposed fashion and radially symmetrical with the driving omni wheel units. So the six restoring omni wheel units are also mounted on three great circles which are orthogonal to each other and the normal directions of the three great circles coincide with the directions of roll, pitch, and yaw, respectively. Each restoring and damping omni wheel unit is controlled by a linear actuator to be operable to contact the inner surface of the outer spherical shell at all times in order to apply restoring and damping moments on the spherical vehicle in a fixed direction relative to the spherical vehicle body-fixed reference frame. Each restoring omni wheel unit is connected with one rotational spring and one rotational damper. Preferably, the rotational springs are machined springs to provide precise deflection rates. The rotational dampers are installed on the shafts of the restoring omni wheels by a mechanism similar to an automobile transmission so that the damping effects are capable to be shifted among different levels during operation just like changing gears in automobiles. The shift of the rotational damper is controlled by a linear actuator mounted on the external surface of the casing of the restoring and damping assembly.

In another embodiment, the air bearing assemblies in this invention may be replaced by ball wheel assemblies with a comparable size. Therefore in this case, the on-board air compressors are not necessary, and the spherical vehicle weight may be decreased. Comparing with the frictionless environment provided by the air bearings, the ball wheel assemblies introduce certain friction damping into this rotational system, i.e. the spherical vehicle.

BRIEF DESCRIPTION OF THE DRAWINGS

The following descriptions of drawings of the preferred embodiments are merely exemplary in nature and are not intended to limit the scope of the invention, its applications, or uses in anyway.

FIG. 1 is a perspective view of the nonlinear vehicle dynamically equivalent simulator with a quarter portion cut-out of the outer sphere to allow a view of the inside structures of the simulator.

FIG. 2 is a side view of the simulator shown in FIG. 1.

FIG. 3 is a top view of the simulator shown in FIG. 1.

FIG. 4 is a front view of the simulator shown in FIG. 1.

FIG. 5 is an exploded view of the outer sphere and the supporting hydraulic platform with controllable vertical motion capability.

FIG. 6 is a section view of the outer sphere and its supporting structure.

FIG. 7 is an exploded view of the outer sphere shown in FIG. 6.

FIG. 8a and FIG. 8b are perspective views at different angles for a supporting structure panel of the outer sphere.

FIG. 9 is a perspective view of the inner spherical skeleton with spike-type supports.

FIG. 10 is a side view of the spherical skeleton shown in FIG. 9.

FIG. 11 is a front view of the spherical skeleton shown in FIG. 9.

FIG. 12 is a top view of the spherical skeleton shown in FIG. 9.

FIG. 13a is a perspective view of the spherical skeleton structure with a reference cube inside the skeleton. FIG. 13b is a perspective view of the spherical skeleton structure without the reference cube. FIG. 13c is perspective section view of a typical frame constructing the spherical skeleton. FIG. 13d is a rear view of a typical four-frame joint of the spherical skeleton. FIG. 13e is a rear view of a typical three-frame joint of the spherical skeleton.

FIG. 14 is an exploded view of a spike-type support of air bearing assembly.

FIG. 15 is a zoom-in perspective view of the spherical skeleton with a driving assembly, a restoring and damping assembly, and two spike-type supports of air bearing assembly.

FIG. 16 is a perspective view of the driving assembly with a pair of omni wheels.

FIG. 17 is a perspective view of the restoring and damping assembly with a pair of omni wheels.

FIG. 18 is a perspective view of the restoring and damping assembly from an angle different with that of FIG. 17.

FIG. 19a is a perspective view of the inside structures of the restoring and damping assembly shown in FIG. 18. FIG. 19b is perspective view of the restoring and damping assembly showing a spring mounting mechanism. FIG. 19c is a section view of A-A plane in FIG. 19b to show details of the spring mounting mechanism for the restoring and damping assembly.

FIG. 20 is an exploded outside view of the restoring and damping assembly shown in FIG. 18.

FIG. 21a is a perspective inside view of the restoring and damping assembly shown in FIG. 18 and FIG. 19a . FIG. 21b is an exploded view of the restoring and damping assembly. FIG. 21c is another exploded view showing the damping assembly.

FIG. 22a is a perspective view of the outer sphere door assembly with the door open. FIG. 22b is a perspective view of the outer sphere door assembly with the door closed.

FIG. 23a is a perspective view of the top portion of the door assembly. FIG. 23b is a perspective view of the bottom portion of the door assembly.

FIG. 24 is a perspective view of the motion simulator cockpit.

FIG. 25 is a perspective view of the spherical skeleton with a shell type screen for visualization.

FIG. 26a is the perspective view of a ball wheel assembly which may be used to replace the air bearing assembly shown in FIG. 14. FIG. 26b is the side view of the ball wheel assembly.

DETAILED DESCRIPTION OF THE EMBODIMENTS

Referring to the drawings, more particularly to FIG. 1, the spherical vehicle 109 is suspended inside the spherical shell made of top half shell 107 and bottom half shell 106. The spherical shell is supported by the vertically movable hydraulic piston 105 and four linear actuators 104 a, 104 b, 104 c (shown in FIG. 2) and 104 d (shown in FIG. 4). The piston 105 is mounted on the top and in the center of the horizontal movable platform 103 which has a plurality of wheels at its bottom. These wheels are movable along a plurality of rails 111 and driven by electrical motors (not shown) controlled by the control system of the simulator. These rails 111 are parallel and mounted equally spaced on top of another platform 102 which is larger than the platform 103 and has a plurality of wheels at its bottom. These wheels are movable along a plurality of rails 110 and driven by electrical motors (not shown) controlled by the control system of the simulator. These rails 110 are parallel and mounted equally spaced on top of another platform 101 which is larger than the platform 102. The orientations of the rails 111 and the rails 110 are orthogonal. Therefore the three translational motions, i.e. surge, sway, and heave are provided by the platforms 103, the platform 102, and the platform 105, respectively. On the top half shell 107, there is a sliding door assembly 108 capable to be opened from outside of the spherical shell to let people in and out of the spherical vehicle 109. FIG. 2 is a side view of the simulator shown in FIG. 1 with the door open showing the pilot cabin. A vertical movable supporting platform includes the piston 105, a round platform 112, and a bowl-like supporting structure 113. A set of screen 114 may be used for showing the virtual reality view of simulations. The platform 101 is on a flat ground of a room which is housing the simulator. FIG. 3 and FIG. 4 are a top view and a front view of the simulator, respectively, showing the detailed layouts. A plurality of air bearing assemblies 115, shown in FIG. 2 and FIG. 4, are mounted on ring beams of the spherical vehicle 109.

Detailed layouts of the spherical shell and its supporting structures are given in FIG. 5, FIG. 6, FIG. 7, FIG. 8a and FIG. 8b . The bottom half spherical shell 106 shown in FIG. 5 includes an outer layer 106 a, a round apex outer layer 106 c, and an inner seamless thin shell layer of half sphere 106 b as shown in FIG. 6. The outer layer 106 a includes 16 identical panels each of which looks like panel 106 a-1 shown in FIG. 8a and FIG. 8b . These 16 panels are fastened together by bolts through the outside frames of the panels as shown in FIG. 8a and FIG. 8b and also fasten together with the round apex outer layer 106 c by a plurality of bolts to become a solid bottom half spherical shell (106 a and 106 c). Preferably, the outer layer panels are made of fiber-reinforced composite materials or the like to provide light weight and enough strength to support the inner thin layer 106 b and in turn to support the weight of the spherical vehicle, and the inner thin layer 106 b is to be made of airtight and hard materials such as fiber-reinforced composite materials or the like, or even metals like aluminum or stainless steel if necessary. The top half spherical shell 107 has similar structures as the bottom half spherical shell 106. The bowl-like supporting structure 113 as shown in FIG. 5, FIG. 6, and FIG. 7 is mounted on the platform 112 by a plurality of vertical screws. The outer layer 106 a, the round apex outer layer 106 c, and the bowl-like supporting structure 113 are fastened together by a plurality of horizontal bolts as shown in FIG. 6. The half sphere seamless thin layer 106 b is bonded with the half outer layer spherical shell (106 a and 106 c) as shown in FIG. 7 to form a solid half spherical shell 106. The top half spherical shell 107 and the bottom half spherical shell 106 joint together by bolts through the frames along the great circles as shown by FIG. 5 to form a solid spherical shell which has airtight and extremely smooth inner surface.

Referring to FIG. 9, FIG. 10, FIG. 11, FIG. 12, FIG. 13a , FIG. 13b , FIG. 13c , FIG. 13d , and FIG. 13e , the spherical vehicle includes spherical skeleton 121 shown in FIG. 13a and FIG. 13 b, 14 air bearing assemblies 115 shown in FIG. 9, six drive assemblies 116 a, 116 b, 116 c, 116 d, 116 e, and 116 f shown in FIG. 9, six restoring and damping assemblies 117 a, 117 b, 117 c, 117 d, 117 e, and 117 f shown in FIG. 9, a pilot cabin support platform 119, pilot models 118, a dashboard 120, and screens 114. The spherical vehicle also contains all the necessary equipment (not shown) for suspending the spherical vehicle, for controlling, and operating the vehicle such as air compressors, batteries, computers, even oxygen tanks (if necessary) and etc. The spherical skeleton 121 shown in FIG. 13a and FIG. 13b includes a plurality of ring beams. Preferably, these ring beams are made of fiber-reinforced composite materials or light metal such as aluminum to provide strong bending strength and light weight. The radiuses of all the ring beams are same. All these ring beams are within the circumscribing sphere of a tetrakis hexahedron based on the inside cube shown in FIG. 13a . The tetrakis hexahedron may be imagined as the inside cube with pyramids on each face. The apex of each pyramid coincides with the centers of the four-ring-beam joints (shown in FIG. 13d ) which are also located on X, Y, and Z axes as shown in FIG. 13a . There are nine ring beams in the example. Three ring beams are located on the XOY, YOZ, and XOZ planes, respectively. The orientations of the other six ring beams may be found by rotating the above three ring beams ±45° about X, Y, and Z axes, respectively. Each ring beam includes two sub-ring beams with U-type cross sections as shown in FIG. 13c . The two sub-ring beams are bonded together side by side to form a solid ring beam in order to provide more bending strength in the middle line as shown in FIG. 13c . The nine ring beams are connected with each other to form a solid spherical skeleton as a truss base for the spherical vehicle as shown in FIG. 13b . FIG. 13d is an underneath view showing a typical joint of four ring beams. FIG. 13e is an underneath view showing a typical joint of three ring beams.

Referring to FIG. 14, each of the air bearing assemblies 115 includes a support post 115 d, a ball connector 115 b, and a convex spherical air bearing 115 a with an air inlet 115 c. The air bearing assemblies are mounted radially outward on the ring beams which construct the skeleton for the spherical vehicle. Preferably, there are 14 identical air bearing assemblies as shown in FIG. 9, FIG. 10, FIG. 11, and FIG. 12. These air bearings are located at the locations of the 14 vertices of the tetrakis hexahedron (not shown) mentioned above. The air bearing is made of porous materials and has a convex spherical curved surface which matches that of the inner surface of the spherical shell. High pressure air from the on-board air compressors is supplied through a hose (not shown) connecting to the air inlet 115 c into the air bearing 115 a to form a thin layer of air. The size of the air bearing 115 a determined by the total weight of the spherical vehicle is large enough to provide enough support to suspend the spherical vehicle when all the 14 air bearings are working at same time. The 14 air bearing assemblies are distributed around the outside of the spherical vehicle in such a way that the spherical vehicle may be suspended inside of the outer spherical shell to allow frictionless motions for the spherical vehicle.

While the embodiment in FIG. 9 shows the use of 14 air bearing assemblies, it will be understood by one of skill in the art that a small or a larger number of air bearing assemblies could also be used to support the spherical vehicle such as, for example, 12 air bearing assemblies located at the vertices of an icosahedron on which a spherical skeleton is based and in this case the three orthogonal ring beams described above located on the XOY, YOZ, and XOZ planes are still needed.

The four-ring-beam joint in FIG. 13d provides a supporting structure in the spherical skeleton with the strongest bending strength. There are six such four-ring-beam joints in the spherical skeleton. There are six identical driving assemblies and six identical restoring and damping assemblies. A typical driving assembly 117 c and a typical restoring and damping assembly 116 c are located close to a four-ring-beam joint shown in FIG. 15. Similarly, the other five driving assemblies and the other five restoring and damping assemblies are located close to the other five four-ring-beam joints, respectively. The six driving assemblies and the six restoring and damping assemblies are mounted on the three ring beams which are located in the XOY, XOZ, and YOZ planes, respectively. Therefore, these three ring beams are orthogonal to each other as shown in FIG. 13 a.

The driving assembly 117 c includes an electrical right-angle DC motor 117 c-1, a pinned support 117 c-5 to restrict horizontal and vertical movements of the motor on a ring beam but allow a rotational movement, two identical omni wheels 117 c-2 and 117 c-3 which are paired up and symmetrically located on each side of the right-angle DC motor as shown in FIG. 16 to provide smooth motion for the spherical vehicle, a linear actuator 117 c-4 and a pinned support 117 c-6 supporting 117 c-4. The omni wheels are specially designed to have continuous alternate rollers (e.g. German patent DE822660) to allow smooth movements for the spherical vehicle. The rollers are made of material that provides excellent traction and control. The pinned supports 117 c-5 and 117 c-6 are aligned with the centerline of the ring beam as shown in FIG. 15. The other end (not shown) of the linear actuator 117 c-4 is connected to a pinned support (not shown) mounted on the outside surface of the square casing of the DC motor 117 c-1 to control the rotation of the drive assembly 117 c about the pinned support 117 c-5 in order to contact and to detach the inner surface of the spherical shell. The rotations (RPM) of the omni wheels are controlled by the DC motors. The normal pressure of the omni wheels on the inner surface of the spherical shell is controlled by the linear actuator 117 c-4. The RPM of the omni wheels and the normal pressure of the omni wheels on the inner surface are adjustable to provide a desired moment on the spherical vehicle. The driving assemblies 117 c and 117 d shown in FIG. 10 are two identical driving units mounted on the ring beam which is in the XOZ plane. These two driving units are paired up and diametrically opposed to each other on the ring beam with the omni wheel rotation axes parallel to the pitch axis of the spherical vehicle as shown in FIG. 10 in order to provide pitch moments on the spherical vehicle. Other driving assemblies 117 a and 117 b (shown in FIGS. 11), 117 e and 117 f (shown in FIG. 12) are mounted in the structure in a similar way as that of 117 c and 117 d. More specifically, the driving assemblies 117 a and 117 b are paired up and mounted on the ring beam within the YOZ plane and in the orientation to provide roll moments on the spherical vehicle as shown in FIG. 11 while the driving assemblies 117 e and 117 f are paired up and mounted on the ring beam within the XOY plane and in the orientation to provide yaw moments on the spherical vehicle as shown in FIG. 12.

Referring to FIG. 17, the restoring and damping assembly 116 c includes a cylindrical outer casing 116 c-1, a square outer casing 116 c-7, a pinned support 116 c-5 to restrict horizontal and vertical movements of the assembly on a ring beam but allow a rotational movement, two identical omni wheels 116 c-2 and 116 c-3 which are symmetrically located on each side of the square outer casing 116 c-7 to provide smooth motions for the spherical vehicle, a linear actuator 116 c-4, a pinned support 116 c-6 supporting 116 c-4, and a pinned support 116 c-8. The pinned supports 116 c-5 and 116 c-6 are aligned with the centerline of the ring beam as shown in FIG. 15. The linear actuator 116 c-4 is to control the rotation movement of the restoring and damping assembly 116 c about the pinned support 116 c-5 in order to contact the inner surface of the outer spherical shell. The omni wheels are connected to a rotational damper 131 (shown in FIG. 19a ) inside the square casing 116 c-7 through a shaft 126 (shown in FIG. 18) and are also connected to a rotational spring 128 (shown in FIG. 19a ) through bevel gears inside the square casing 116 c-7 shown in FIG. 18. The restoring and damping assemblies 116 c and 116 d as shown in FIG. 10 are two identical assemblies and mounted on the ring beam which is in the XOZ plane. These two assemblies are paired up and diametrically opposed to each other on the ring beam with the omni wheel rotation axes parallel to the pitch axis of the spherical vehicle as shown in FIG. 10 in order to provide restoring and damping pitch moments on the spherical vehicle. Other restoring and damping assemblies 116 a and 116 b (shown in FIGS. 11), 116 e and 116 f (shown in FIG. 12) are mounted in the structure in a similar way as that of 116 c and 116 d. More specifically, the restoring and damping assemblies 116 a and 116 b are paired up and mounted on the ring beam within the YOZ plane and in the orientation to provide roll restoring and damping moments on the spherical vehicle as shown in FIG. 11 while the restoring and damping assemblies 116 e and 116 f are paired up and mounted on the ring beam within the XOY plane and in the orientation to provide yaw restoring and damping moments on the spherical vehicle as shown in FIG. 12. The restoring and damping assemblies 116 a, 116 b, 116 c, 116 d, 116 e, and 116 f contact the inner surface of the outer spherical shell at all the time during operation of the spherical vehicle. Therefore the rotational movements of the omni wheels are passive subject to the rotational movement of the spherical vehicle, the rotational springs and the rotational dampers. The omni wheels of the restoring and damping assemblies are identical with the omni wheels of the driving assemblies.

Referring to FIG. 18, the square casing 116 c-7 has a circular opening connecting to the cylindrical casing 116 c-1 and a lid 123 on which a linear actuator 124 is mounted. The cylindrical casing 116 c-1 also has a lid 122. A machined rotational spring 128 is installed inside the cylindrical casing 116 c-1 as shown in FIG. 19a and FIG. 19b . One end of 128 is connected to 116 c-1 through two bolt mechanisms 132 a and 132 b which are smoothly slidable in slots 161 a and 161 b (not shown), respectively as shown in FIG. 19b . The two slots 161 a and 161 b (not shown) are diametrically opposed to each other and located longitudinally in the inside surface of 116 c-1. The two slots 161 a and 161 b (not shown) are about half depth of the shell thickness of 116 c-1 with certain length and width depending on the characteristics of the spring 128 to restrict the rotational motion of the spring 128 on this end but release the longitudinal stress created during the rotational movements of the spring 128. A section view of A-A plane in FIG. 19b is given in FIG. 19c to show the detailed layout of the mechanism. The other end of the spring 128 is fastened to a shaft 136 as shown in FIG. 19c . The shaft 136 is fixed in place by a ball bearing 129 (FIG. 19a , FIG. 21a , and FIG. 21b ) in the wall of the square casing 116 c-7 (shown in FIG. 18) and is connected to another shaft 126 by bevel gears 139 and 140 as shown in FIG. 21b to transfer the rotational motions between the shaft 126 and the shaft 136. Although straight bevel gear is demonstrated in FIGS. 21b and 21c , other bevel gears could be used, such as Zerol, spiral, or hypoid bevel gears. The two omni wheels are installed rigidly on the two ends of the shaft 126 as shown in FIG. 18. In such way, the rotational kinetic energy of the omni wheels 116 c-2 and 116 c-3 (FIG. 18) may be transferred to the potential energy of the spring 128 (FIG. 19a , FIG. 21b ) and vice versa.

The typical rotational damper 131 with a center hole which is larger than the shaft 126 and has a synchronizer cone teeth arrangement as shown in FIG. 21b and FIG. 21c . The damper 131 is supported by two larger radial ball bearings 130 a and 130 b so that it suspends over the shaft 126 as shown in FIG. 21a . As shown in FIG. 21b and FIG. 21c , a hub 141 is fixed to the shaft 126, and a sleeve 142 that is free to slide over the hub 141 is connected with a shift fork 143. A synchronizer ring 144 is located between the hub 141 and the damper 131 as shown in FIG. 21b and FIG. 21c . The shift fork 143 is fixed to a shift rod 134 (shown in FIG. 21a ) which is controlled by the linear actuator 124 through a connector 127. The shift rod 134 is slidable through two holes one of which is in partition wall 133 and the other hole is in a ring support 137 (shown in FIG. 21a ) which is fixed on the inside surface (not shown) of the lid 123 (FIG. 20). The connector 127 as shown in FIG. 20 links the shift rod 134 (FIG. 21a ) inside the square casing 116 c-7 (FIG. 17) to the linear actuator 124 mounted on the outside surface of the lid 123 (FIG. 20) through a rectangular hole 135 on the lid 123 as shown in FIG. 20. The other end of the linear actuator 124 is connected to a pinned support 125 on the outside surface of the lid 123 (FIG. 20). Therefore, when the linear actuator 124 moves the sleeve 142 to connect the hub 141 with the synchronizer cone teeth on the damper 131, a desired locking mechanism would be achieved and the rotational damper 131 is engaged in the assembly. In the other way around, the linear actuator 124 may move the sleeve 142 to disconnect the hub 141 with the damper 131 so that the damper is disengaged in the assembly. As shown in FIG. 20, there is a neck mechanism in the halfway through the hole 135 to serve as a support for the connector 127 to work efficiently in moving the shift rod 134 in both ways.

The door assembly 108 (FIG. 1) of the outer spherical shell is illustrated in FIG. 22a and FIG. 22b . The assembly 108 (FIG. 1) is capable to slide along the track bounded by a top track 145 and a bottom track 147 as shown in FIG. 22a . The top track 145 is mounted on outside frames 107 a (FIG. 22b ) of the top half spherical shell 107 (FIG. 1) with the help of two brackets 146. The lower track 147 is mounted on the outside frames 106 a (FIG. 22b ) of the bottom spherical shell 106 (FIG. 1) with the help of three brackets 146. There are two door frames in this assembly. One is the frame 107 a-d (FIG. 22a ) which is also the original frame of one bottom panel of the spherical shell 107 (FIG. 1) with the middle plate cut out as shown in FIG. 22a . The other frame is a sliding frame 156 which is holding a door panel 155 as shown in FIG. 22a . The sliding frame 156 and the door panel 155 are sliding together as one piece as shown in FIG. 22a . At least two sets of wheel assembly 149 (FIG. 23a ) are mounted vertically at the top of the sliding frame 156 and at least two sets of wheel assembly 148 (only one set is shown in FIG. 23a ) are mounted almost horizontally at the top of the sliding frame 156. Similarly, at least two sets of wheel assembly 151 (only one set is shown in FIG. 23b ) are mounted vertically at the bottom of the sliding frame 156 and at least two sets of wheel assembly 150 (only one set is shown in FIG. 23b ) are mounted horizontally on the bottom of the sliding frame 156. At least four hinge assemblies 152 (FIG. 22a , FIG. 22b ) are mounted on the four sides of the sliding frame 156, respectively to allow the door panel 155 to be opened and close easily as shown in FIG. 22a where the door panel 155 is opened and slides away with the frame 156, and as shown in FIG. 22b where the door panel 155 is closed. There are four slots 157 a, 157 b, 157 c (not shown), and 157 d (not shown) on the two vertical frame sides of the door 155 and there are four same size slots 158 a (not shown), 158 b (not shown), 158 c, and 158 d on the two vertical sides of the frame 107 a-d as shown in FIG. 22a . Four flat door bolts 154 would be pushed into slot 158 a, 158 b, 158 c, and 158 d, respectively to lock the door panel 155 in place to form a perfect shell as shown in FIG. 22b . A door handle 153 (FIG. 22a and FIG. 22b ) is located in the center of the door panel 155.

A platform 119 is fixed to the ring beams horizontally inside of the spherical skeleton as shown in FIG. 10 and FIG. 11. The pilot cabin on top of the platform 119 as shown in FIG. 24 includes pilot models 118, dashboard 120, screens 114, control columns 159, and other necessary equipment (not shown) such as batteries, air compressors, computers etc. The mass distributions of all the equipment on board the spherical vehicle needs to be carefully designed and arranged to meet a certain requirement described below.

Due to the space limitation of any motion simulators, translational motions (surge, sway, and heave) cannot be simulated 100%. For example heights and distances traveled by an aircraft or speeds of an aircraft in translational directions may not be able to be simulated. However, for a short period of time translational accelerations of a vehicle in surge, sway, and heave may be able to be simulated by moving the platform 103, the platform 102, and the piston 105 as shown in FIG. 1, respectively in order to apply desired inertial force effects on trainees on board the spherical vehicle 109. For rotational motions, there is no such space limitation in this invention which is able to simulate 100% rotational dynamics of vehicles including, but not limited to, aircrafts, automobiles, and ships. As we know it is the rotational motion characteristics that are the most crucial for the safety of these vehicles. To obtain valid results from this invention, the spherical vehicle must be designed and constructed in a special manner that will ensure that its rotational motions are identical with rotational motions that would be exhibited by a full scale vehicle. The spherical vehicle is not geometrically scaled replicas of the original vehicle, but a dynamically scaled model. For that purpose, a scaling factor needs to be determined first. The moments of inertias, the restoring coefficients, and the damping coefficients of the spherical vehicle and the driving moments acting on the spherical vehicle in this invention have to be at a same scale comparing with the counterparts (the original vehicle) to be simulated. More specifically, assume the rotational motions (φ,θ,ψ) of the original vehicle, for example an aircraft, are governed by the following equations in the principal inertia axes reference frame.

I _(x) {umlaut over (φ)}+b ₁ {dot over (φ)}+k ₁φ=(I _(y) −I _(z)){dot over (θ)}{dot over (ψ)}+M ₁₁(t),  Math. 11

I _(y) {umlaut over (θ)}+b ₂ {dot over (θ)}+k ₂θ=(I _(z) −I _(x)){dot over (φ)}{dot over (ψ)}+M ₂₁(t),  Math. 12

I _(z) {umlaut over (ψ)}+b ₃ {dot over (ψ)}+k ₃ψ=(I _(z) −I _(y)){dot over (φ)}{dot over (θ)}+M ₃₁(t),  Math. 13

wherein, I_(x), I_(y), and I_(z) are the moment of inertias of the original vehicle about the principal axes of X, Y and Z, respectively, b₁, b₂, and b₃ are the damping coefficients for roll, pitch, and yaw, respectively, k₁, k₂, and k₃ are the restoring coefficients for roll, pitch, and yaw, respectively, M₁₁, M₂₁, and M₃₁ are the external moments along the roll, pitch, and yaw directions, respectively. In order to have dynamic equivalence between the full scale original vehicle and the spherical vehicle (or called subscale model) in this invention, let us multiply a constant scaling factor Δ to the above equations, we obtain.

λI _(x) {umlaut over (φ)}+λb ₁ {dot over (φ)}+λk ₁φ=(λI _(y) −λI _(z)){dot over (θ)}{dot over (ψ)}+λM ₁₁(t),  Math. 14

λI _(y) {umlaut over (θ)}+λb ₂ {dot over (θ)}+λk ₂θ=(λI _(z) −λI _(x)){dot over (φ)}{dot over (ψ)}+λM ₂₁(t),  Math. 15

λI _(z) {umlaut over (ψ)}+λb ₃ {dot over (ψ)}+λk ₃ψ=(λI _(x) −λI _(y)){dot over (φ)}{dot over (θ)}+λM ₃₁(t).  Math. 16

The spherical vehicle in this invention is designed to have moments of inertia about the principal inertia axes X, Y, and Z as λI_(x), λI_(y), and λI_(z), respectively; the damping coefficients in roll, pitch, and yaw directions as λb₁, λb₂, and λb₃, respectively; the restoring coefficients in roll, pitch, and yaw directions as, λk₁, λk₂, and λk₃ respectively; and the moments acting in roll, pitch, and yaw directions as λM₁₁, λM₂₁, and λM₃₁, respectively. In summary, all these parameters are simply decreased in a same scale from that of the original values. The center of gravity of the spherical vehicle coincides with the geometric center of the outer spherical shell. Therefore the rotational motion dynamics of the full scale original vehicle would be identical with that of the spherical vehicle designed according to the above requirements because the governing equations Math. 11, Math.12, and Math. 13 of the former are actually identical with the governing equations Math. 14, Math. 15, and Math.16 of the latter. The scaling factor λ could be ranging from very small, say 0.0001, for a very heavy vehicle to about 1 for a small vehicle or even larger than 1 for tinny vehicle depending the applications.

For a ship application, the moments of inertias I_(x), I_(y), and I_(z) should include the added mass effects and the yaw restoring coefficient k₃ should be set to zero. Therefore the dynamics of the simulator would be conservative in terms of the nonlinear instability threshold value comparing with that of the original full scale ship.

A plurality of ventilation ports, i.e. small holes (not shown) may be provided on the top portion of the top half spherical shell 107 to permit air circulation for the occupants.

In another embodiment, a shell screen 160 may be mounted on the inside of the spherical skeleton 121 as shown in FIG. 25 to replace the screen 114 (FIG. 9) for showing the virtual reality view of simulations. In this case, the screen 114 may become windows of the pilot cabin.

In yet another embodiment, the air bearing assemblies 115 (FIG. 9 and FIG. 14) may be replaced by omni-directional ball bearing assembly 170 as shown in FIG. 26a and FIG. 26b . In this case, the on board air compressors are not needed.

In an alternative embodiment, the platform 112 (FIG. 5) is mounted to the ground of the room that houses the simulator. This embodiment shows the version of the simulator that gives up three translational motions in exchange for a simpler design.

It should be understood that the detailed description and specific examples, while indicating the preferred embodiment, are intended for purposes of illustration only and it should be understood that it may be embodied in a large variety of forms different from the one specifically shown and described without departing from the scope and spirit of the invention. This motion simulator in this invention can be as small or as large as is necessary for applications. It should be also understood that the invention is not limited to the specific features shown, but that the means and construction herein disclosed comprise a preferred form of putting the invention into effect, and the invention therefore claimed in any of its forms of modifications within the legitimate and valid scope of the appended claims. 

What is claimed is:
 1. A motion simulating device comprising: a. a spherical shell with smooth inner surface mounted on the ground; b. a spherical vehicle suspending within said spherical shell, wherein said spherical vehicle including a plurality of ring beams for forming vehicle's base truss, c. a plurality of bearing assemblies located around exterior of said beams for suspending said spherical vehicle within said spherical shell, wherein each bearing assembly includes a bearing and a support post which is connected on one end to exterior of a said ring beam and on the other end to said bearing, d. a plurality of driving assemblies located around exterior of said ring beams for rotationally driving said vehicle with respect to said vehicle's roll, pitch, and yaw axes, wherein each driving assembly includes motor-driven omni wheels and a linear actuator, e. a plurality of restoring assemblies located around exterior of said ring beams for rotationally restoring positions of said vehicle with respect to said vehicle's roll, pitch, and yaw axes, wherein each restoring assembly includes restoring omni wheels, a rotational spring, and a linear actuator, f. a plurality of damping assemblies connectable to said restoring omni wheels for damping said vehicle's motions with respect to said vehicle's roll, pitch, and yaw axes, wherein each damping assembly includes a rotational damper and a shift gear mechanism controlled by a linear actuator for engaging and disengaging said damper, g. a simulating pilot cabin mounted within said spherical vehicle; h. a method for constructing said spherical shell; i. a method for constructing said spherical vehicle; j. a method for designing a dynamically equivalent mechanical model for full scale vehicle rotational dynamics;
 2. The motion simulating device of claim 1 further comprising a means utilizing said linear actuators for controlling the normal pressures of said motor-driven omni wheels and said restoring omni wheels on the inner surface of said spherical shell.
 3. The motion simulating device of claim 1, wherein said bearings comprise air bearings and required air compressors;
 4. The motion simulating device of claim 1, wherein said bearings comprise omni-directional ball bearings;
 5. The motion simulating device of claim 1 further comprising a shell screen mounted on the inside of said ring beams for visual simulation purpose.
 6. A motion simulating device comprising: a. a spherical shell which has smooth inner surface and mounted on three controllable translational motion platforms, b. a spherical vehicle suspending within said spherical shell, wherein said spherical vehicle including a plurality of ring beams for forming vehicle's base truss, c. a plurality of bearing assemblies located around exterior of said beams for suspending said spherical vehicle within said spherical shell, wherein each bearing assembly includes a bearing and a support post which is connected on one end to exterior of a said ring beam and on the other end to said bearing, d. a plurality of driving assemblies located around exterior of said ring beams for rotationally driving said vehicle with respect to said vehicle's roll, pitch, and yaw axes, wherein each driving assembly includes motor-driven omni wheels and a linear actuator, e. a plurality of restoring assemblies located around exterior of said ring beams for rotationally restoring positions of said vehicle with respect to said vehicle's roll, pitch, and yaw axes, wherein each restoring assembly includes restoring omni wheels, a rotational spring, and a linear actuator, f. a plurality of damping assemblies connectable to said restoring omni wheels for damping said vehicle's motions with respect to said vehicle's roll, pitch, and yaw axes, wherein each damping assembly includes a rotational damper and a shift gear mechanism controlled by a linear actuator for engaging and disengaging said damper, g. a simulating pilot cabin mounted within said spherical vehicle; h. a method for constructing said spherical shell; i. a method for constructing said spherical vehicle; j. a method for designing a dynamically equivalent mechanical model for full scale vehicle rotational dynamics;
 7. The motion simulating device of claim 6 further comprising a means utilizing said linear actuators for controlling the normal pressure of said motor-driven omni wheels and said restoring omni wheels on the inner surface of said spherical shell.
 8. The motion simulating device of claim 6, wherein said bearings comprise air bearings and required air compressors;
 9. The motion simulating device of claim 6, wherein said bearings comprise omni-directional ball bearings;
 10. The motion simulating device of claim 6 further comprising a shell screen mounted inside said spherical vehicle skeleton for visual simulation purpose. 